Estimation of the linear relationship between the measurements of two methods with proportional errors.

The linear relationship between the measurements of two methods is estimated on the basis of a weighted errors-in-variables regression model that takes into account a proportional relationship between standard deviations of error distributions and true variable levels. Weights are estimated by an interative procedure. As shown by simulations, the regression procedure yields practically unbiased slope estimates in realistic situations. Standard errors of slope and location difference estimations are derived by the jackknife principle. For illustration, the linear relationship is estimated between the measurements of two albumin methods with proportional errors.

[1]  Douglas G. Altman,et al.  Measurement in Medicine: The Analysis of Method Comparison Studies , 1983 .

[2]  M. Kendall,et al.  The advanced theory of statistics , 1945 .

[3]  Gabrielle E. Kelly,et al.  Use of the Structural Equations Model in Assessing the Reliability of a New Measurement Technique , 1985 .

[4]  V. D. Barnett,et al.  Fitting Straight Lines—The Linear Functional Relationship with Replicated Observations , 1970 .

[5]  R. Carroll,et al.  Variance Function Estimation , 1987 .

[6]  Gabrielle E. Kelly,et al.  The influence function in the errors in variables problem , 1981 .

[7]  W A Sadler,et al.  A computer program for variance function estimation, with particular reference to immunoassay data. , 1987, Computers and biomedical research, an international journal.

[8]  P. Sprent,et al.  A Generalized Least‐Squares Approach to Linear Functional Relationships , 1966 .

[9]  J. W. Ross,et al.  The effect of analyte and analyte concentration upon precision estimates in clinical chemistry. , 1976, American journal of clinical pathology.

[10]  C Kay,et al.  Dose-interpolation of immunoassay data: uncertainties associated with curve-fitting. , 1986, Statistics in medicine.

[11]  Elise de Doncker,et al.  D01 Chapter-Numerical Algorithms Group, in samenwerking met de andere D01-contributors. 1) NAG Fortran Mini Manual, Mark 8, D01 18p., , 1981 .

[12]  J. Mandel,et al.  The Statistical Analysis of Experimental Data. , 1965 .

[13]  Anders Hald,et al.  Statistical Theory with Engineering Applications , 1952 .

[14]  Changbao Wu,et al.  Jackknife, Bootstrap and Other Resampling Methods in Regression Analysis , 1986 .

[15]  N Gochman,et al.  Incorrect least-squares regression coefficients in method-comparison analysis. , 1979, Clinical chemistry.

[16]  W. Sadler,et al.  A method for direct estimation of imprecision profiles, with reference to immunoassay data. , 1988, Clinical chemistry.

[17]  D. Altman,et al.  STATISTICAL METHODS FOR ASSESSING AGREEMENT BETWEEN TWO METHODS OF CLINICAL MEASUREMENT , 1986, The Lancet.